The news was first reported by the Sporting News.
Green is expected to ink a one-year deal with the team that originally selected him with the No. 18 pick in the 2005 draft. He spent two seasons with Boston before being dealt to the Minnesota Timberwolves as part of the Kevin Garnett deal in 2007.
The 30-year-old Green averaged 8.9 points per game in 69 appearances for the Heat last season, including 14 games as a starter. An erratic season for Green saw the nine-year veteran go from being a high-scoring sixth man for the Heat in the first half of the season to barely playing over long stretches entering the playoffs. Despite those inconsistencies with his role, Green repeatedly said he hoped to remain in Miami long term.
Stability, however, has evaded Green for most of an NBA career in which he's played for the Celtics, Houston Rockets, Timberwolves, Dallas Mavericks, Brooklyn Nets, Indiana Pacers and Phoenix Suns. He signed a one-year deal for the veterans minimum with the Heat last summer.
Green has shot 36.1 percent beyond the 3-point arc for his career. During the 2013-14 season with Phoenix, Green shot 40 percent while hoisting a career-high 510 attempts.
Information from ESPN's Michael Wallace was used in this report.